Click here to close now.

Welcome!

Apache Authors: Elizabeth White, AppDynamics Blog, Roger Strukhoff, Liz McMillan, Carmen Gonzalez

Related Topics: Java IoT, @MicroservicesE Blog, Adobe Flex, IoT User Interface, Apache

Java IoT: Article

Why Averages Are Inadequate, and Percentiles Are Great

Averages are ineffective because they are too simplistic and one-dimensional

Anyone who ever monitored or analyzed an application uses or has used averages. They are simple to understand and calculate. We tend to ignore just how wrong the picture is that averages paint of the world. To emphasis the point let me give you a real-world example outside of the performance space that I read recently in a newspaper.

The article was explaining that the average salary in a certain region in Europe was 1900 Euro's (to be clear this would be quite good in that region!). However when looking closer they found out that the majority, namely 9 out of 10 people, only earned around 1000 Euros and one would earn 10.000 (I over simplified this of course, but you get the idea). If you do the math you will see that the average of this is indeed 1900, but we can all agree that this does not represent the "average" salary as we would use the word in day to day live. So now let's apply this thinking to application performance.

The Average Response Time
The average response time is by far the most commonly used metric in application performance management. We assume that this represents a "normal" transaction, however this would only be true if the response time is always the same (all transaction run at equal speed) or the response time distribution is roughly bell curved.

A Bell curve represents the "normal" distribution of response times in which the average and the median are the same. It rarely ever occurs in real applications

In a Bell Curve the average (mean) and median are the same. In other words observed performance would represent the majority (half or more than half) of the transactions.

In reality most applications have few very heavy outliers; a statistician would say that the curve has a long tail. A long tail does not imply many slow transactions, but few that are magnitudes slower than the norm.

This is a typical Response Time Distribution with few but heavy outliers - it has a long tail. The average here is dragged to the right by the long tail.

We recognize that the average no longer represents the bulk of the transactions but can be a lot higher than the median.

You can now argue that this is not a problem as long as the average doesn't look better than the median. I would disagree, but let's look at another real-world scenario experienced by many of our customers:

This is another typical Response Time Distribution. Here we have quite a few very fast transactions that drag the average to the left of the actual median

In this case a considerable percentage of transactions are very, very fast (10-20 percent), while the bulk of transactions are several times slower. The median would still tell us the true story, but the average all of a sudden looks a lot faster than most of our transactions actually are. This is very typical in search engines or when caches are involved - some transactions are very fast, but the bulk are normal. Another reason for this scenario are failed transactions, more specifically transactions that failed fast. Many real-world applications have a failure rate of 1-10 percent (due to user errors or validation errors). These failed transactions are often magnitudes faster than the real ones and consequently distorted an average.

Of course performance analysts are not stupid and regularly try to compensate with higher frequency charts (compensating by looking at smaller aggregates visually) and by taking in minimum and maximum observed response times. However we can often only do this if we know the application very well, those unfamiliar with the application might easily misinterpret the charts. Because of the depth and type of knowledge required for this, it's difficult to communicate your analysis to other people - think how many arguments between IT teams have been caused by this. And that's before we even begin to think about communicating with business stakeholders!

A better metric by far are percentiles, because they allow us to understand the distribution. But before we look at percentiles, let's take a look a key feature in every production monitoring solution: Automatic Baselining and Alerting.

Automatic Baselining and Alerting
In real-world environments, performance gets attention when it is poor and has a negative impact on the business and users. But how can we identify performance issues quickly to prevent negative effects? We cannot alert on every slow transaction, since there are always some. In addition, most operations teams have to maintain a large number of applications and are not familiar with all of them, so manually setting thresholds can be inaccurate, quite painful and time-consuming.

The industry has come up with a solution called Automatic Baselining. Baselining calculates out the "normal" performance and only alerts us when an application slows down or produces more errors than usual. Most approaches rely on averages and standard deviations.

Without going into statistical details, this approach again assumes that the response times are distributed over a bell curve:

The Standard Deviation represents 33% of all transactions with the mean as the middle. 2xStandard Deviation represents 66% and thus the majority, everything outside could be considered an outlier. However most real world scenarios are not bell curved...

Typically, transactions that are outside two times standard deviation are treated as slow and captured for analysis. An alert is raised if the average moves significantly. In a bell curve this would account for the slowest 16.5 percent (and you can of course adjust that); however; if the response time distribution does not represent a bell curve, it becomes inaccurate. We either end up with a lot of false positives (transactions that are a lot slower than the average but when looking at the curve lie within the norm) or we miss a lot of problems (false negatives). In addition if the curve is not a bell curve, then the average can differ a lot from the median; applying a standard deviation to such an average can lead to quite a different result than you would expect. To work around this problem these algorithms have many tunable variables and a lot of "hacks" for specific use cases.

Why I Love Percentiles
A percentile tells me which part of the curve I am looking at and how many transactions are represented by that metric. To visualize this look at the following chart:

This chart shows the 50th and 90th percentile along with the average of the same transaction. It shows that the average is influenced far mor heavily by the 90th, thus by outliers and not by the bulk of the transactions

The green line represents the average. As you can see it is very volatile. The other two lines represent the 50th and 90th percentile. As we can see the 50th percentile (or median) is rather stable but has a couple of jumps. These jumps represent real performance degradation for the majority (50%) of the transactions. The 90th percentile (this is the start of the "tail") is a lot more volatile, which means that the outliers slowness depends on data or user behavior. What's important here is that the average is heavily influenced (dragged) by the 90th percentile, the tail, rather than the bulk of the transactions.

If the 50th percentile (median) of a response time is 500ms that means that 50% of my transactions are either as fast or faster than 500ms. If the 90th percentile of the same transaction is at 1000ms it means that 90% are as fast or faster and only 10% are slower. The average in this case could either be lower than 500ms (on a heavy front curve), a lot higher (long tail) or somewhere in between. A percentile gives me a much better sense of my real world performance, because it shows me a slice of my response time curve.

For exactly that reason percentiles are perfect for automatic baselining. If the 50th percentile moves from 500ms to 600ms I know that 50% of my transactions suffered a 20% performance degradation. You need to react to that.

In many cases we see that the 75th or 90th percentile does not change at all in such a scenario. This means the slow transactions didn't get any slower, only the normal ones did. Depending on how long your tail is the average might not have moved at all in such a scenario.!

In other cases we see the 98th percentile degrading from 1s to 1.5 seconds while the 95th is stable at 900ms. This means that your application as a whole is stable, but a few outliers got worse, nothing to worry about immediately. Percentile-based alerts do not suffer from false positives, are a lot less volatile and don't miss any important performance degradations! Consequently a baselining approach that uses percentiles does not require a lot of tuning variables to work effectively.

The screenshot below shows the Median (50th Percentile) for a particular transaction jumping from about 50ms to about 500ms and triggering an alert as it is significantly above the calculated baseline (green line). The chart labeled "Slow Response Time" on the other hand shows the 90th percentile for the same transaction. These "outliers" also show an increase in response time but not significant enough to trigger an alert.

Here we see an automatic baselining dashboard with a violation at the 50th percentile. The violation is quite clear, at the same time the 90th percentile (right upper chart) does not violate. Because the outliers are so much slower than the bulk of the transaction an average would have been influenced by them and would not have have reacted quite as dramatically as the 50th percentile. We might have missed this clear violation!

How Can We Use Percentiles for Tuning?
Percentiles are also great for tuning, and giving your optimizations a particular goal. Let's say that something within my application is too slow in general and I need to make it faster. In this case I want to focus on bringing down the 90th percentile. This would ensure sure that the overall response time of the application goes down. In other cases I have unacceptably long outliers I want to focus on bringing down response time for transactions beyond the 98th or 99th percentile (only outliers). We see a lot of applications that have perfectly acceptable performance for the 90th percentile, with the 98th percentile being magnitudes worse.

In throughput oriented applications on the other hand I would want to make the majority of my transactions very fast, while accepting that an optimization makes a few outliers slower. I might therefore make sure that the 75th percentile goes down while trying to keep the 90th percentile stable or not getting a lot worse.

I could not make the same kind of observations with averages, minimum and maximum, but with percentiles they are very easy indeed.

Conclusion
Averages are ineffective because they are too simplistic and one-dimensional. Percentiles are a really great and easy way of understanding the real performance characteristics of your application. They also provide a great basis for automatic baselining, behavioral learning and optimizing your application with a proper focus. In short, percentiles are great!

More Stories By Michael Kopp

Michael Kopp has over 12 years of experience as an architect and developer in the Enterprise Java space. Before coming to CompuwareAPM dynaTrace he was the Chief Architect at GoldenSource, a major player in the EDM space. In 2009 he joined dynaTrace as a technology strategist in the center of excellence. He specializes application performance management in large scale production environments with special focus on virtualized and cloud environments. His current focus is how to effectively leverage BigData Solutions and how these technologies impact and change the application landscape.

Comments (1) View Comments

Share your thoughts on this story.

Add your comment
You must be signed in to add a comment. Sign-in | Register

In accordance with our Comment Policy, we encourage comments that are on topic, relevant and to-the-point. We will remove comments that include profanity, personal attacks, racial slurs, threats of violence, or other inappropriate material that violates our Terms and Conditions, and will block users who make repeated violations. We ask all readers to expect diversity of opinion and to treat one another with dignity and respect.


Most Recent Comments
rtalexander 11/21/12 12:58:00 AM EST

Hey, could you post a reference or two that covers the theory and/or practicalities of the approach you describe?

Thanks!

@ThingsExpo Stories
The 4th International Internet of @ThingsExpo, co-located with the 17th International Cloud Expo - to be held November 3-5, 2015, at the Santa Clara Convention Center in Santa Clara, CA - announces that its Call for Papers is open. The Internet of Things (IoT) is the biggest idea since the creation of the Worldwide Web more than 20 years ago.
The enterprise market will drive IoT device adoption over the next five years. In his session at @ThingsExpo, John Greenough, an analyst at BI Intelligence, division of Business Insider, will analyze how companies will adopt IoT products and the associated cost of adopting those products. John Greenough is the lead analyst covering the Internet of Things for BI Intelligence- Business Insider’s paid research service. Numerous IoT companies have cited his analysis of the IoT. Prior to joining BI Intelligence, he worked analyzing bank technology for Corporate Insight and The Clearing House Pay...
As the Internet of Things unfolds, mobile and wearable devices are blurring the line between physical and digital, integrating ever more closely with our interests, our routines, our daily lives. Contextual computing and smart, sensor-equipped spaces bring the potential to walk through a world that recognizes us and responds accordingly. We become continuous transmitters and receivers of data. In his session at @ThingsExpo, Andrew Bolwell, Director of Innovation for HP's Printing and Personal Systems Group, discussed how key attributes of mobile technology – touch input, sensors, social, and ...
All major researchers estimate there will be tens of billions devices - computers, smartphones, tablets, and sensors - connected to the Internet by 2020. This number will continue to grow at a rapid pace for the next several decades. With major technology companies and startups seriously embracing IoT strategies, now is the perfect time to attend @ThingsExpo, June 9-11, 2015, at the Javits Center in New York City. Learn what is going on, contribute to the discussions, and ensure that your enterprise is as "IoT-Ready" as it can be
SYS-CON Events announced today that BMC will exhibit at SYS-CON's 16th International Cloud Expo®, which will take place on June 9-11, 2015, at the Javits Center in New York City, NY. BMC delivers software solutions that help IT transform digital enterprises for the ultimate competitive business advantage. BMC has worked with thousands of leading companies to create and deliver powerful IT management services. From mainframe to cloud to mobile, BMC pairs high-speed digital innovation with robust IT industrialization – allowing customers to provide amazing user experiences with optimized IT per...
The world is at a tipping point where the technology, the device and global adoption are converging to such a point that we will see an explosion of a world where smartphone devices not only allow us to talk to each other, but allow for communication between everything – serving as a central hub from which we control our world – MediaTek is at the heart of both driving this and allowing the markets to drive this reality forward themselves. The next wave of consumer gadgets is here – smart, connected, and small. If your ambitions are big, so are ours. In his session at @ThingsExpo, Jack Hu, D...
Today’s enterprise is being driven by disruptive competitive and human capital requirements to provide enterprise application access through not only desktops, but also mobile devices. To retrofit existing programs across all these devices using traditional programming methods is very costly and time consuming – often prohibitively so. In his session at @ThingsExpo, Jesse Shiah, CEO, President, and Co-Founder of AgilePoint Inc., discussed how you can create applications that run on all mobile devices as well as laptops and desktops using a visual drag-and-drop application – and eForms-buildi...
SYS-CON Events announced today that MetraTech, now part of Ericsson, has been named “Silver Sponsor” of SYS-CON's 16th International Cloud Expo®, which will take place on June 9–11, 2015, at the Javits Center in New York, NY. Ericsson is the driving force behind the Networked Society- a world leader in communications infrastructure, software and services. Some 40% of the world’s mobile traffic runs through networks Ericsson has supplied, serving more than 2.5 billion subscribers.
The Internet of Things is not only adding billions of sensors and billions of terabytes to the Internet. It is also forcing a fundamental change in the way we envision Information Technology. For the first time, more data is being created by devices at the edge of the Internet rather than from centralized systems. What does this mean for today's IT professional? In this Power Panel at @ThingsExpo, moderated by Conference Chair Roger Strukhoff, panelists will addresses this very serious issue of profound change in the industry.
The multi-trillion economic opportunity around the "Internet of Things" (IoT) is emerging as the hottest topic for investors in 2015. As we connect the physical world with information technology, data from actions, processes and the environment can increase sales, improve efficiencies, automate daily activities and minimize risk. In his session at @ThingsExpo, Ed Maguire, Senior Analyst at CLSA Americas, will describe what is new and different about IoT, explore financial, technological and real-world impact across consumer and business use cases. Why now? Significant corporate and venture...
"People are a lot more knowledgeable about APIs now. There are two types of people who work with APIs - IT people who want to use APIs for something internal and the product managers who want to do something outside APIs for people to connect to them," explained Roberto Medrano, Executive Vice President at SOA Software, in this SYS-CON.tv interview at Cloud Expo, held Nov 4–6, 2014, at the Santa Clara Convention Center in Santa Clara, CA.
WebRTC defines no default signaling protocol, causing fragmentation between WebRTC silos. SIP and XMPP provide possibilities, but come with considerable complexity and are not designed for use in a web environment. In his session at @ThingsExpo, Matthew Hodgson, technical co-founder of the Matrix.org, discussed how Matrix is a new non-profit Open Source Project that defines both a new HTTP-based standard for VoIP & IM signaling and provides reference implementations.
SYS-CON Events announced today that O'Reilly Media has been named “Media Sponsor” of SYS-CON's 16th International Cloud Expo®, which will take place on June 9–11, 2015, at the Javits Center in New York City, NY. O'Reilly Media spreads the knowledge of innovators through its books, online services, magazines, and conferences. Since 1978, O'Reilly Media has been a chronicler and catalyst of cutting-edge development, homing in on the technology trends that really matter and spurring their adoption by amplifying "faint signals" from the alpha geeks who are creating the future. An active participa...
There will be 150 billion connected devices by 2020. New digital businesses have already disrupted value chains across every industry. APIs are at the center of the digital business. You need to understand what assets you have that can be exposed digitally, what their digital value chain is, and how to create an effective business model around that value chain to compete in this economy. No enterprise can be complacent and not engage in the digital economy. Learn how to be the disruptor and not the disruptee.
2015 predictions circa 1970: houses anticipate our needs and adapt, city infrastructure is citizen and situation aware, office buildings identify and preprocess you. Today smart buildings have no such collective conscience, no shared set of fundamental services to identify, predict and synchronize around us. LiveSpace and M2Mi are changing that. LiveSpace Smart Environment devices deliver over the M2Mi IoT Platform real time presence, awareness and intent analytics as a service to local connected devices. In her session at @ThingsExpo, Sarah Cooper, VP Business of Development at M2Mi, will d...
Thanks to widespread Internet adoption and more than 10 billion connected devices around the world, companies became more excited than ever about the Internet of Things in 2014. Add in the hype around Google Glass and the Nest Thermostat, and nearly every business, including those from traditionally low-tech industries, wanted in. But despite the buzz, some very real business questions emerged – mainly, not if a device can be connected, or even when, but why? Why does connecting to the cloud create greater value for the user? Why do connected features improve the overall experience? And why do...
Almost everyone sees the potential of Internet of Things but how can businesses truly unlock that potential. The key will be in the ability to discover business insight in the midst of an ocean of Big Data generated from billions of embedded devices via Systems of Discover. Businesses will also need to ensure that they can sustain that insight by leveraging the cloud for global reach, scale and elasticity.
Imagine a world where targeting, attribution, and analytics are just as intrinsic to the physical world as they currently are to display advertising. Advances in technologies and changes in consumer behavior have opened the door to a whole new category of personalized marketing experience based on direct interactions with products. The products themselves now have a voice. What will they say? Who will control it? And what does it take for brands to win in this new world? In his session at @ThingsExpo, Zack Bennett, Vice President of Customer Success at EVRYTHNG, will answer these questions a...
With major technology companies and startups seriously embracing IoT strategies, now is the perfect time to attend @ThingsExpo in Silicon Valley. Learn what is going on, contribute to the discussions, and ensure that your enterprise is as "IoT-Ready" as it can be! Internet of @ThingsExpo, taking place Nov 3-5, 2015, at the Santa Clara Convention Center in Santa Clara, CA, is co-located with 17th Cloud Expo and will feature technical sessions from a rock star conference faculty and the leading industry players in the world. The Internet of Things (IoT) is the most profound change in personal an...
We’re entering a new era of computing technology that many are calling the Internet of Things (IoT). Machine to machine, machine to infrastructure, machine to environment, the Internet of Everything, the Internet of Intelligent Things, intelligent systems – call it what you want, but it’s happening, and its potential is huge. IoT is comprised of smart machines interacting and communicating with other machines, objects, environments and infrastructures. As a result, huge volumes of data are being generated, and that data is being processed into useful actions that can “command and control” thi...